1. Technical Field
The invention relates to scanning probe microscopes, such as atomic force microscopes or magnetic resonance force microscopes. More particularly, the invention relates to control systems used for operating a scanning probe microscope.
2. Description of the Prior Art
Since the invention of the scanning tunneling microscope (STM), a variety of other scanning probe microscopes have been developed. Among these, scanning force microscopy (SFM) is the most prominent technique. In SFM, interaction forces acting between a scanned probe tip and a sample are exploited for imaging purposes, similar to the tunneling current in STM. Examples of SFM are atomic force microscopy (AFM), electric force microscopy (EFM), and magnetic resonance force microscopy (MRFM).
The key component in SFM is a tip on a cantilever, which acts as a force sensor. See, e.g. Marohn et al. (1998), Garner et al. (2004), and Struckmeier et al. (2006). When the tip is brought close to the surface of the sample under investigation, the interaction force between the tip and the sample causes a deflection of the cantilever, which behaves as a soft spring. It can be shown that the force gradients acting on the cantilever, in effect, change the cantilever's spring constant, and hence its resonance frequency. See, e.g. Albrecht et al. (1991) and Dürig et al. (1997). By measuring this change in resonance frequency of the cantilever, the interaction force can be measured.
There are several different ways to determine changes in the resonance frequency. One such method is slope detection, where the cantilever is driven off resonance and a change in the resonance frequency is registered as a change in the amplitude of the cantilever response. Another method is phase detection, where the cantilever is driven at resonance, and a change in the resonant frequency is recorded as a change in the phase of the response. Yet another method uses the cantilever as a frequency-determining element in a positive feedback loop. See Albrecht et al. (1991) for a comparison of these methods. The voltage in the loop is demodulated to give the frequency of the cantilever. The frequency-modulation (FM) approach has the advantage of following cantilever frequency shifts which are large compared to the natural width of the cantilever resonance. Another advantage is that its bandwidth is governed only by the characteristics of the FM demodulator.
As with many imaging applications, the more sensitive the measuring apparatus is, the more accuracy it can measure, and the better the quality of its image. This is definitely true for scanned-force microscopy (SFM): the better it can measure the interaction force, or the higher the force sensitivity, the better the quality of its image. This better image quality typically translates to the ability to measure smaller features of the sample one is imaging, i.e. a higher resolution. In SFM, the mechanical properties of the cantilever, which are determined by its dimensions and material properties, ultimately define the sensitivity of the measurement system. However, for a cantilever of given dimensions and material, control of the cantilever motion is instrumental in extracting the best possible information from the measurement system.
Control of a cantilever involves three key components:
1. A sensor to detect the motion of the cantilever, e.g. an optical interferometer that detects the position of the cantilever tip as a function of time;
2. A mechanism to force-actuate the motion of the cantilever, e.g. a piezo element that exerts a force at the base of the cantilever; and
3. An algorithm that computes the force actuation based on the sensor measurements. This algorithm can be a combination of different control loops.
Typically, different parts of the algorithm are exercised for different types of experiments one wishes to perform with the cantilever. Typical control experiments include (but are not limited to):                Excitation of the cantilever via positive feedback control while locking to the cantilever resonance frequency. This experiment measures the cantilever frequency and shifts in the resonant frequency, which are used for imaging surface topology.        Optimal feedback control of the cantilever that attenuates the thermo-mechanical fluctuations from the observed cantilever motion to minimize vibration of the cantilever tip.        Ring-down measurements and observation of thermal fluctuations to calculate the mechanical properties of the cantilever, such as quality factor, resonance frequency, and spring constant.        Amplitude control of the cantilever tip position, i.e. maintaining a constant amplitude of the observed cantilever motion in the face of frequency changes and/or thermal fluctuations.        Frequency-shift control of the cantilever tip position, i.e. maintaining a constant frequency-shift of the observed cantilever motion by changing the distance, e.g. height, between the cantilever and the sample.        
Currently, the preferred method of implementation of these control experiments is the use of analog components, mainly because analog components are inexpensive and fast. However, there are a number of disadvantages to the use of analog components:                Each time the mechanical properties of the cantilever change significantly, such as its resonance frequency, some of the analog components must be replaced to maintain stability and performance.        Similarly, tuning of control experiments requires either adjusting potentiometers or replacing analog components. Besides the tedium and required skill of doing this, there is also a level of uncertainty involved in the final implementation.        Analog components suffer from thermal drift as the ambient temperature changes during an experiment. This can influence the outcome of an experiment if the experiment is performed over a long period of time. This is especially crucial when imaging, which typically takes a long time. That is, points in the image taken at a later time could be distorted by thermal drift with respect to points taken at the beginning of the image.        Each of the experiments described above requires a different set of analog components and, thus, the work rack fills up quickly with all the different components, breadboards, and other equipment used for the experiment.        
Given these disadvantages, it is no surprise that some people started looking into a digital alternative, i.e. the use of a digital circuit such as a Digital Signal Processor (DSP) or Field Programmable Gate Array (FPGA) for implementing at least some of the abovementioned control experiments. One such an example is the work of Loppacher et al. (1998) who implemented a Phase-Lock-Loop (PLL) with a digitally synthesized clock, and which was able to resolve a small 5 MHz change in a 280 kHz sinusoid with a PLL bandwidth of 500 Hz. Another example is the use of GNU radio, which uses a combination of FPGA and DSP to implement the Optimal Control experiment. A sampling rate of roughly 250 kHz is achieved with 16 bit accuracy, see J. Jacky et al. (2006). Also, there are a number of commercial circuits available, such as frequency counters, lock-in amplifiers, and digital PLL's, which can be used in some of the abovementioned experiments.
The ideal digital controller would be able to do all of the experiments described above and more. It would be comparable in speed to analog components, especially when it comes to experiments that resolve the smallest possible frequency shift. It would be compact in a sense that one small circuit would replace all of the analog components, as well as other units such as lock-in amplifiers, frequency counters, etc., basically providing one box that would replace an entire rack of components. It would have minimal thermal drift, at least an order of magnitude less than analog components. It would have a number of meaningful tuning parameters available, as well as a user-friendly graphical interface (GUI) for adjusting those tuning parameters and performing different types of experiments. Neither the described digital implementations in the literature, nor any of the commercially available digital circuits can meet all of these requirements.
It would be advantageous to provide an approach and implementation that addresses all of these limitations.